I am very familiar with duplex being the standard for medical installations. My question is if there is a flow controller, or a flow meter with a valve, installed on an oxygen pipeline to the hospital, do there need to be two? Would having only one be a violation of NFPA 99?

Are we talking about Primary Source Equipment or Secondary Patient Care Equipment  

The flow controller is a flow meter. It does not do any good to duplex the flow meter when the rest of the system is simplex. Ideally you would have to have two completely separate system to consider it duplex or it can be simplex with a backup (cylinder reserve). When you need to work on the system you go on the reserve cylinders.

To shove my oar in here, no standard requires a flow controller (to Al's point - I am referring to the proposed 2018).  The flow controller is a technical requirement of the technology being used. Redundancy (to Robert's point) would be a necessity if the machine depended on it for proper operation, or if it was required to properly operate the primary - secondary - reserve cascade, but not otherwise.  Many manufacturers of concentrators use a simple inline orafice or backpressure regulator to acheive the same result.

To Robert's point, the provision of a flow limiting device within the "black box" of the concentrator supply source would be a manufacturer's decision, because it is about how the machine operates.  Flow restriction in the pipeline (e.g. patient side of the source valve) would be inappropriate, but not here.